Kolmijako

#include <bits/stdc++.h>

typedef long long ll;

#define M 1000000007
#define N (1 << 18)

using namespace std;

int ans[101];
int n;
ll sum;

void brute(int cn) {
    if (cn == n) {
        int sums[3] = {0};

        for (int i = 0; i < n; ++i) {
            sums[ans[i] - 1] += i + 1;
        }
        ll ts = 0;
        for (int i = 0; i < 3; ++i) {
            ts += sums[i];
        }
        //if (ts != sum) cout << "ERR";
        //cout << sums[0] << ", " << sums[1] << ", " << sums[2] << endl;
        int t = sum / 3;
        if (sums[0] == t - 1 && sums[1] == t && sums[2] == t + 1) {
            for (int i = 0; i < n; ++i) {
                cout << ans[i] << " ";
            }
            cout << "\n";
            exit(0);
        }
    } else {
        ans[cn] = 1;
        brute(cn + 1);
        ans[cn] = 2;
        brute(cn + 1);
        ans[cn] = 3;
        brute(cn + 1);
    }
}

int main() {
	ios_base::sync_with_stdio(false);
	cin.tie(0);
	cin >> n;
    sum = n * (n + 1) / 2;
	if (sum % 3 != 0) {
        cout << "IMPOSSIBLE";
        return 0;
    }

    brute(0);

	return 0;
}

Test 1

Group: 1, 2

Verdict: ACCEPTED

Test 2

Group: 1, 2

Verdict: ACCEPTED

Test 3

Group: 1, 2

Verdict: ACCEPTED

Test 4

Group: 1, 2

Verdict: ACCEPTED

Test 5

Group: 1, 2

Verdict: ACCEPTED

Test 6

Group: 1, 2

Verdict: ACCEPTED

Test 7

Group: 1, 2

Verdict: ACCEPTED

Test 8

Group: 1, 2

Verdict: ACCEPTED

Test 9

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 10

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 11

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 12

Group: 2

Verdict: ACCEPTED

Test 13

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 14

Group: 2

Verdict: TIME LIMIT EXCEEDED

Test 15

Group: 2

Verdict: ACCEPTED